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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef BIGUNSIGNED_H</span></div><div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor">#define BIGUNSIGNED_H</span></div><div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;</div><div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#include &quot;NumberlikeArray.hh&quot;</span></div><div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;</div><div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">/* A BigUnsigned object represents a nonnegative integer of size limited only by</span></div><div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment"> * available memory.  BigUnsigneds support most mathematical operators and can</span></div><div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment"> * be converted to and from most primitive integer types.</span></div><div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment"> *</span></div><div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment"> * The number is stored as a NumberlikeArray of unsigned longs as if it were</span></div><div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment"> * written in base 256^sizeof(unsigned long).  The least significant block is</span></div><div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment"> * first, and the length is such that the most significant block is nonzero. */</span></div><div class="line"><a name="l00013"></a><span class="lineno"><a class="line" href="class_big_unsigned.html">   13</a></span>&#160;<span class="keyword">class </span><a class="code" href="class_big_unsigned.html">BigUnsigned</a> : <span class="keyword">protected</span> <a class="code" href="class_numberlike_array.html">NumberlikeArray</a>&lt;unsigned long&gt; {</div><div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;</div><div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">public</span>:</div><div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;    <span class="comment">// Enumeration for the result of a comparison.</span></div><div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;    <span class="keyword">enum</span> CmpRes { less = -1, equal = 0, greater = 1 };</div><div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;</div><div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;    <span class="comment">// BigUnsigneds are built with a Blk type of unsigned long.</span></div><div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;    <span class="keyword">typedef</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> Blk;</div><div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;</div><div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;    <span class="keyword">typedef</span> NumberlikeArray&lt;Blk&gt;::Index Index;</div><div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;    <span class="keyword">using</span> <a class="code" href="class_numberlike_array.html">NumberlikeArray&lt;Blk&gt;::N</a>;</div><div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;</div><div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="keyword">protected</span>:</div><div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    <span class="comment">// Creates a BigUnsigned with a capacity; for internal use.</span></div><div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a>(<span class="keywordtype">int</span>, Index c) : <a class="code" href="class_numberlike_array.html">NumberlikeArray&lt;Blk&gt;</a>(0, c) {}</div><div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;</div><div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <span class="comment">// Decreases len to eliminate any leading zero blocks.</span></div><div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    <span class="keywordtype">void</span> zapLeadingZeros() { </div><div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;        <span class="keywordflow">while</span> (len &gt; 0 &amp;&amp; blk[len - 1] == 0)</div><div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;            len--;</div><div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    }</div><div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;</div><div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="keyword">public</span>:</div><div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    <span class="comment">// Constructs zero.</span></div><div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a>() : <a class="code" href="class_numberlike_array.html">NumberlikeArray&lt;Blk&gt;</a>() {}</div><div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;</div><div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <span class="comment">// Copy constructor</span></div><div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a>(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) : <a class="code" href="class_numberlike_array.html">NumberlikeArray&lt;Blk&gt;</a>(x) {}</div><div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;</div><div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    <span class="comment">// Assignment operator</span></div><div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    <span class="keywordtype">void</span> operator=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) {</div><div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        <a class="code" href="class_numberlike_array.html">NumberlikeArray&lt;Blk&gt;::operator =</a>(x);</div><div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    }</div><div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;</div><div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;    <span class="comment">// Constructor that copies from a given array of blocks.</span></div><div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a>(<span class="keyword">const</span> Blk *b, Index blen) : <a class="code" href="class_numberlike_array.html">NumberlikeArray&lt;Blk&gt;</a>(b, blen) {</div><div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;        <span class="comment">// Eliminate any leading zeros we may have been passed.</span></div><div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;        zapLeadingZeros();</div><div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    }</div><div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;</div><div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    <span class="comment">// Destructor.  NumberlikeArray does the delete for us.</span></div><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    ~<a class="code" href="class_big_unsigned.html">BigUnsigned</a>() {}</div><div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    </div><div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <span class="comment">// Constructors from primitive integer types</span></div><div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">long</span>  x);</div><div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a>(         <span class="keywordtype">long</span>  x);</div><div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>   x);</div><div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a>(         <span class="keywordtype">int</span>   x);</div><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">short</span> x);</div><div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a>(         <span class="keywordtype">short</span> x);</div><div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;<span class="keyword">protected</span>:</div><div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;    <span class="comment">// Helpers</span></div><div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">class</span> X&gt; <span class="keywordtype">void</span> initFromPrimitive      (X x);</div><div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">class</span> X&gt; <span class="keywordtype">void</span> initFromSignedPrimitive(X x);</div><div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;<span class="keyword">public</span>:</div><div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;</div><div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    <span class="comment">/* Converters to primitive integer types</span></div><div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="comment">     * The implicit conversion operators caused trouble, so these are now</span></div><div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;<span class="comment">     * named. */</span></div><div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span>  toUnsignedLong () <span class="keyword">const</span>;</div><div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    <span class="keywordtype">long</span>           toLong         () <span class="keyword">const</span>;</div><div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>   toUnsignedInt  () <span class="keyword">const</span>;</div><div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    <span class="keywordtype">int</span>            toInt          () <span class="keyword">const</span>;</div><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">short</span> toUnsignedShort() <span class="keyword">const</span>;</div><div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <span class="keywordtype">short</span>          toShort        () <span class="keyword">const</span>;</div><div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;<span class="keyword">protected</span>:</div><div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    <span class="comment">// Helpers</span></div><div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">class</span> X&gt; X convertToSignedPrimitive() <span class="keyword">const</span>;</div><div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">class</span> X&gt; X convertToPrimitive      () <span class="keyword">const</span>;</div><div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;<span class="keyword">public</span>:</div><div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;</div><div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    <span class="comment">// BIT/BLOCK ACCESSORS</span></div><div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;</div><div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    <span class="comment">// Expose these from NumberlikeArray directly.</span></div><div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    <span class="keyword">using</span> <a class="code" href="class_numberlike_array.html">NumberlikeArray&lt;Blk&gt;::getCapacity</a>;</div><div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <span class="keyword">using</span> <a class="code" href="class_numberlike_array.html">NumberlikeArray&lt;Blk&gt;::getLength</a>;</div><div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;</div><div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    <span class="comment">/* Returns the requested block, or 0 if it is beyond the length (as if</span></div><div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;<span class="comment">     * the number had 0s infinitely to the left). */</span></div><div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;    Blk getBlock(Index i)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> i &gt;= len ? 0 : blk[i]; }</div><div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    <span class="comment">/* Sets the requested block.  The number grows or shrinks as necessary. */</span></div><div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    <span class="keywordtype">void</span> setBlock(Index i, Blk newBlock);</div><div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;</div><div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    <span class="comment">// The number is zero if and only if the canonical length is zero.</span></div><div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    <span class="keywordtype">bool</span> isZero()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="class_numberlike_array.html">NumberlikeArray&lt;Blk&gt;::isEmpty</a>(); }</div><div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;</div><div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    <span class="comment">/* Returns the length of the number in bits, i.e., zero if the number</span></div><div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;<span class="comment">     * is zero and otherwise one more than the largest value of bi for</span></div><div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;<span class="comment">     * which getBit(bi) returns true. */</span></div><div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;    Index bitLength() <span class="keyword">const</span>;</div><div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    <span class="comment">/* Get the state of bit bi, which has value 2^bi.  Bits beyond the</span></div><div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;<span class="comment">     * number&#39;s length are considered to be 0. */</span></div><div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    <span class="keywordtype">bool</span> getBit(Index bi)<span class="keyword"> const </span>{</div><div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;        <span class="keywordflow">return</span> (getBlock(bi / N) &amp; (Blk(1) &lt;&lt; (bi % N))) != 0;</div><div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    }</div><div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    <span class="comment">/* Sets the state of bit bi to newBit.  The number grows or shrinks as</span></div><div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;<span class="comment">     * necessary. */</span></div><div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;    <span class="keywordtype">void</span> setBit(Index bi, <span class="keywordtype">bool</span> newBit);</div><div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;</div><div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    <span class="comment">// COMPARISONS</span></div><div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;</div><div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    <span class="comment">// Compares this to x like Perl&#39;s &lt;=&gt;</span></div><div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    CmpRes compareTo(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) <span class="keyword">const</span>;</div><div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;</div><div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    <span class="comment">// Ordinary comparison operators</span></div><div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    <span class="keywordtype">bool</span> operator ==(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x)<span class="keyword"> const </span>{</div><div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="class_numberlike_array.html">NumberlikeArray&lt;Blk&gt;::operator ==</a>(x);</div><div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    }</div><div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    <span class="keywordtype">bool</span> operator !=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x)<span class="keyword"> const </span>{</div><div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="class_numberlike_array.html">NumberlikeArray&lt;Blk&gt;::operator !=</a>(x);</div><div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;    }</div><div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    <span class="keywordtype">bool</span> operator &lt; (<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> compareTo(x) == less   ; }</div><div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    <span class="keywordtype">bool</span> operator &lt;=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> compareTo(x) != greater; }</div><div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;    <span class="keywordtype">bool</span> operator &gt;=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> compareTo(x) != less   ; }</div><div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;    <span class="keywordtype">bool</span> operator &gt; (<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> compareTo(x) == greater; }</div><div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;</div><div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;    <span class="comment">/*</span></div><div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;<span class="comment">     * BigUnsigned and BigInteger both provide three kinds of operators.</span></div><div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;<span class="comment">     * Here ``big-integer&#39;&#39; refers to BigInteger or BigUnsigned.</span></div><div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;<span class="comment">     *</span></div><div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;<span class="comment">     * (1) Overloaded ``return-by-value&#39;&#39; operators:</span></div><div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="comment">     *     +, -, *, /, %, unary -, &amp;, |, ^, &lt;&lt;, &gt;&gt;.</span></div><div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;<span class="comment">     * Big-integer code using these operators looks identical to code using</span></div><div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;<span class="comment">     * the primitive integer types.  These operators take one or two</span></div><div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;<span class="comment">     * big-integer inputs and return a big-integer result, which can then</span></div><div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;<span class="comment">     * be assigned to a BigInteger variable or used in an expression.</span></div><div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;<span class="comment">     * Example:</span></div><div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;<span class="comment">     *     BigInteger a(1), b = 1;</span></div><div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;<span class="comment">     *     BigInteger c = a + b;</span></div><div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;<span class="comment">     *</span></div><div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;<span class="comment">     * (2) Overloaded assignment operators:</span></div><div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;<span class="comment">     *     +=, -=, *=, /=, %=, flipSign, &amp;=, |=, ^=, &lt;&lt;=, &gt;&gt;=, ++, --.</span></div><div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;<span class="comment">     * Again, these are used on big integers just like on ints.  They take</span></div><div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;<span class="comment">     * one writable big integer that both provides an operand and receives a</span></div><div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;<span class="comment">     * result.  Most also take a second read-only operand.</span></div><div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;<span class="comment">     * Example:</span></div><div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;<span class="comment">     *     BigInteger a(1), b(1);</span></div><div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;<span class="comment">     *     a += b;</span></div><div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;<span class="comment">     *</span></div><div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;<span class="comment">     * (3) Copy-less operations: `add&#39;, `subtract&#39;, etc.</span></div><div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;<span class="comment">     * These named methods take operands as arguments and store the result</span></div><div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;<span class="comment">     * in the receiver (*this), avoiding unnecessary copies and allocations.</span></div><div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;<span class="comment">     * `divideWithRemainder&#39; is special: it both takes the dividend from and</span></div><div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;<span class="comment">     * stores the remainder into the receiver, and it takes a separate</span></div><div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;<span class="comment">     * object in which to store the quotient.  NOTE: If you are wondering</span></div><div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;<span class="comment">     * why these don&#39;t return a value, you probably mean to use the</span></div><div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;<span class="comment">     * overloaded return-by-value operators instead.</span></div><div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;<span class="comment">     * </span></div><div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;<span class="comment">     * Examples:</span></div><div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;<span class="comment">     *     BigInteger a(43), b(7), c, d;</span></div><div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;<span class="comment">     *</span></div><div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;<span class="comment">     *     c = a + b;   // Now c == 50.</span></div><div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;<span class="comment">     *     c.add(a, b); // Same effect but without the two copies.</span></div><div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;<span class="comment">     *</span></div><div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;<span class="comment">     *     c.divideWithRemainder(b, d);</span></div><div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;<span class="comment">     *     // 50 / 7; now d == 7 (quotient) and c == 1 (remainder).</span></div><div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;<span class="comment">     *</span></div><div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;<span class="comment">     *     // ``Aliased&#39;&#39; calls now do the right thing using a temporary</span></div><div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;<span class="comment">     *     // copy, but see note on `divideWithRemainder&#39;.</span></div><div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;<span class="comment">     *     a.add(a, b); </span></div><div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;<span class="comment">     */</span></div><div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;</div><div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    <span class="comment">// COPY-LESS OPERATIONS</span></div><div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;</div><div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    <span class="comment">// These 8: Arguments are read-only operands, result is saved in *this.</span></div><div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    <span class="keywordtype">void</span> add(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;a, <span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;b);</div><div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    <span class="keywordtype">void</span> subtract(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;a, <span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;b);</div><div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;    <span class="keywordtype">void</span> multiply(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;a, <span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;b);</div><div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;    <span class="keywordtype">void</span> bitAnd(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;a, <span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;b);</div><div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;    <span class="keywordtype">void</span> bitOr(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;a, <span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;b);</div><div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;    <span class="keywordtype">void</span> bitXor(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;a, <span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;b);</div><div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;    <span class="comment">/* Negative shift amounts translate to opposite-direction shifts,</span></div><div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;<span class="comment">     * except for -2^(8*sizeof(int)-1) which is unimplemented. */</span></div><div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;    <span class="keywordtype">void</span> bitShiftLeft(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;a, <span class="keywordtype">int</span> b);</div><div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;    <span class="keywordtype">void</span> bitShiftRight(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;a, <span class="keywordtype">int</span> b);</div><div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;</div><div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    <span class="comment">/* `a.divideWithRemainder(b, q)&#39; is like `q = a / b, a %= b&#39;.</span></div><div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;<span class="comment">     * / and % use semantics similar to Knuth&#39;s, which differ from the</span></div><div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;<span class="comment">     * primitive integer semantics under division by zero.  See the</span></div><div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;<span class="comment">     * implementation in BigUnsigned.cc for details.</span></div><div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;<span class="comment">     * `a.divideWithRemainder(b, a)&#39; throws an exception: it doesn&#39;t make</span></div><div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;<span class="comment">     * sense to write quotient and remainder into the same variable. */</span></div><div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;    <span class="keywordtype">void</span> divideWithRemainder(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;b, <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;q);</div><div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;</div><div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;    <span class="comment">/* `divide&#39; and `modulo&#39; are no longer offered.  Use</span></div><div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;<span class="comment">     * `divideWithRemainder&#39; instead. */</span></div><div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;</div><div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;    <span class="comment">// OVERLOADED RETURN-BY-VALUE OPERATORS</span></div><div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> operator +(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) <span class="keyword">const</span>;</div><div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> operator -(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) <span class="keyword">const</span>;</div><div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> operator *(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) <span class="keyword">const</span>;</div><div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> operator /(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) <span class="keyword">const</span>;</div><div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> operator %(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) <span class="keyword">const</span>;</div><div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    <span class="comment">/* OK, maybe unary minus could succeed in one case, but it really</span></div><div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;<span class="comment">     * shouldn&#39;t be used, so it isn&#39;t provided. */</span></div><div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> operator &amp;(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) <span class="keyword">const</span>;</div><div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> operator |(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) <span class="keyword">const</span>;</div><div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> operator ^(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) <span class="keyword">const</span>;</div><div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> operator &lt;&lt;(<span class="keywordtype">int</span> b) <span class="keyword">const</span>;</div><div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> operator &gt;&gt;(<span class="keywordtype">int</span> b) <span class="keyword">const</span>;</div><div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;</div><div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;    <span class="comment">// OVERLOADED ASSIGNMENT OPERATORS</span></div><div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;    <span class="keywordtype">void</span> operator +=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x);</div><div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;    <span class="keywordtype">void</span> operator -=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x);</div><div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;    <span class="keywordtype">void</span> operator *=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x);</div><div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;    <span class="keywordtype">void</span> operator /=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x);</div><div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    <span class="keywordtype">void</span> operator %=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x);</div><div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    <span class="keywordtype">void</span> operator &amp;=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x);</div><div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;    <span class="keywordtype">void</span> operator |=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x);</div><div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    <span class="keywordtype">void</span> operator ^=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x);</div><div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;    <span class="keywordtype">void</span> operator &lt;&lt;=(<span class="keywordtype">int</span> b);</div><div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;    <span class="keywordtype">void</span> operator &gt;&gt;=(<span class="keywordtype">int</span> b);</div><div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;</div><div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;    <span class="comment">/* INCREMENT/DECREMENT OPERATORS</span></div><div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;<span class="comment">     * To discourage messy coding, these do not return *this, so prefix</span></div><div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;<span class="comment">     * and postfix behave the same. */</span></div><div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;    <span class="keywordtype">void</span> operator ++(   );</div><div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    <span class="keywordtype">void</span> operator ++(<span class="keywordtype">int</span>);</div><div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;    <span class="keywordtype">void</span> operator --(   );</div><div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;    <span class="keywordtype">void</span> operator --(<span class="keywordtype">int</span>);</div><div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;</div><div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;    <span class="comment">// Helper function that needs access to BigUnsigned internals</span></div><div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;    <span class="keyword">friend</span> Blk getShiftedBlock(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;num, Index x,</div><div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;            <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y);</div><div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;</div><div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;    <span class="comment">// See BigInteger.cc.</span></div><div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">class</span> X&gt;</div><div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;    <span class="keyword">friend</span> X convertBigUnsignedToPrimitiveAccess(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;a);</div><div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;};</div><div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;</div><div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;<span class="comment">/* Implementing the return-by-value and assignment operators in terms of the</span></div><div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;<span class="comment"> * copy-less operations.  The copy-less operations are responsible for making</span></div><div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;<span class="comment"> * any necessary temporary copies to work around aliasing. */</span></div><div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;</div><div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;<span class="keyword">inline</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> BigUnsigned::operator +(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x)<span class="keyword"> const </span>{</div><div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> ans;</div><div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;    ans.add(*<span class="keyword">this</span>, x);</div><div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;    <span class="keywordflow">return</span> ans;</div><div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;}</div><div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;<span class="keyword">inline</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> BigUnsigned::operator -(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x)<span class="keyword"> const </span>{</div><div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> ans;</div><div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;    ans.subtract(*<span class="keyword">this</span>, x);</div><div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;    <span class="keywordflow">return</span> ans;</div><div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;}</div><div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;<span class="keyword">inline</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> BigUnsigned::operator *(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x)<span class="keyword"> const </span>{</div><div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> ans;</div><div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;    ans.multiply(*<span class="keyword">this</span>, x);</div><div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;    <span class="keywordflow">return</span> ans;</div><div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;}</div><div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;<span class="keyword">inline</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> BigUnsigned::operator /(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x)<span class="keyword"> const </span>{</div><div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;    <span class="keywordflow">if</span> (x.isZero()) <span class="keywordflow">throw</span> <span class="stringliteral">&quot;BigUnsigned::operator /: division by zero&quot;</span>;</div><div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> q, r;</div><div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;    r = *<span class="keyword">this</span>;</div><div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;    r.divideWithRemainder(x, q);</div><div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;    <span class="keywordflow">return</span> q;</div><div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;}</div><div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;<span class="keyword">inline</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> BigUnsigned::operator %(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x)<span class="keyword"> const </span>{</div><div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;    <span class="keywordflow">if</span> (x.isZero()) <span class="keywordflow">throw</span> <span class="stringliteral">&quot;BigUnsigned::operator %: division by zero&quot;</span>;</div><div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> q, r;</div><div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;    r = *<span class="keyword">this</span>;</div><div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;    r.divideWithRemainder(x, q);</div><div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;    <span class="keywordflow">return</span> r;</div><div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;}</div><div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;<span class="keyword">inline</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> BigUnsigned::operator &amp;(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x)<span class="keyword"> const </span>{</div><div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> ans;</div><div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;    ans.bitAnd(*<span class="keyword">this</span>, x);</div><div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    <span class="keywordflow">return</span> ans;</div><div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;}</div><div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;<span class="keyword">inline</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> BigUnsigned::operator |(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x)<span class="keyword"> const </span>{</div><div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> ans;</div><div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;    ans.bitOr(*<span class="keyword">this</span>, x);</div><div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;    <span class="keywordflow">return</span> ans;</div><div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;}</div><div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;<span class="keyword">inline</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> BigUnsigned::operator ^(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x)<span class="keyword"> const </span>{</div><div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> ans;</div><div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;    ans.bitXor(*<span class="keyword">this</span>, x);</div><div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;    <span class="keywordflow">return</span> ans;</div><div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;}</div><div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;<span class="keyword">inline</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> BigUnsigned::operator &lt;&lt;(<span class="keywordtype">int</span> b)<span class="keyword"> const </span>{</div><div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> ans;</div><div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;    ans.bitShiftLeft(*<span class="keyword">this</span>, b);</div><div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;    <span class="keywordflow">return</span> ans;</div><div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;}</div><div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;<span class="keyword">inline</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> BigUnsigned::operator &gt;&gt;(<span class="keywordtype">int</span> b)<span class="keyword"> const </span>{</div><div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> ans;</div><div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;    ans.bitShiftRight(*<span class="keyword">this</span>, b);</div><div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;    <span class="keywordflow">return</span> ans;</div><div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;}</div><div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;</div><div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> BigUnsigned::operator +=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) {</div><div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;    add(*<span class="keyword">this</span>, x);</div><div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;}</div><div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> BigUnsigned::operator -=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) {</div><div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;    subtract(*<span class="keyword">this</span>, x);</div><div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;}</div><div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> BigUnsigned::operator *=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) {</div><div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;    multiply(*<span class="keyword">this</span>, x);</div><div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;}</div><div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> BigUnsigned::operator /=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) {</div><div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;    <span class="keywordflow">if</span> (x.isZero()) <span class="keywordflow">throw</span> <span class="stringliteral">&quot;BigUnsigned::operator /=: division by zero&quot;</span>;</div><div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;    <span class="comment">/* The following technique is slightly faster than copying *this first</span></div><div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;<span class="comment">     * when x is large. */</span></div><div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> q;</div><div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;    divideWithRemainder(x, q);</div><div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;    <span class="comment">// *this contains the remainder, but we overwrite it with the quotient.</span></div><div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;    *<span class="keyword">this</span> = q;</div><div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;}</div><div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> BigUnsigned::operator %=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) {</div><div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;    <span class="keywordflow">if</span> (x.isZero()) <span class="keywordflow">throw</span> <span class="stringliteral">&quot;BigUnsigned::operator %=: division by zero&quot;</span>;</div><div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;    <a class="code" href="class_big_unsigned.html">BigUnsigned</a> q;</div><div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;    <span class="comment">// Mods *this by x.  Don&#39;t care about quotient left in q.</span></div><div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;    divideWithRemainder(x, q);</div><div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;}</div><div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> BigUnsigned::operator &amp;=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) {</div><div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;    bitAnd(*<span class="keyword">this</span>, x);</div><div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;}</div><div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> BigUnsigned::operator |=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) {</div><div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;    bitOr(*<span class="keyword">this</span>, x);</div><div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;}</div><div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> BigUnsigned::operator ^=(<span class="keyword">const</span> <a class="code" href="class_big_unsigned.html">BigUnsigned</a> &amp;x) {</div><div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;    bitXor(*<span class="keyword">this</span>, x);</div><div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;}</div><div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> BigUnsigned::operator &lt;&lt;=(<span class="keywordtype">int</span> b) {</div><div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;    bitShiftLeft(*<span class="keyword">this</span>, b);</div><div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;}</div><div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> BigUnsigned::operator &gt;&gt;=(<span class="keywordtype">int</span> b) {</div><div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;    bitShiftRight(*<span class="keyword">this</span>, b);</div><div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;}</div><div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;</div><div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;<span class="comment">/* Templates for conversions of BigUnsigned to and from primitive integers.</span></div><div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;<span class="comment"> * BigInteger.cc needs to instantiate convertToPrimitive, and the uses in</span></div><div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;<span class="comment"> * BigUnsigned.cc didn&#39;t do the trick; I think g++ inlined convertToPrimitive</span></div><div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;<span class="comment"> * instead of generating linkable instantiations.  So for consistency, I put</span></div><div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;<span class="comment"> * all the templates here. */</span></div><div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;</div><div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;<span class="comment">// CONSTRUCTION FROM PRIMITIVE INTEGERS</span></div><div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;</div><div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;<span class="comment">/* Initialize this BigUnsigned from the given primitive integer.  The same</span></div><div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;<span class="comment"> * pattern works for all primitive integer types, so I put it into a template to</span></div><div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;<span class="comment"> * reduce code duplication.  (Don&#39;t worry: this is protected and we instantiate</span></div><div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;<span class="comment"> * it only with primitive integer types.)  Type X could be signed, but x is</span></div><div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;<span class="comment"> * known to be nonnegative. */</span></div><div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> X&gt;</div><div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;<span class="keywordtype">void</span> BigUnsigned::initFromPrimitive(X x) {</div><div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;    <span class="keywordflow">if</span> (x == 0)</div><div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;        ; <span class="comment">// NumberlikeArray already initialized us to zero.</span></div><div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;    <span class="keywordflow">else</span> {</div><div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;        <span class="comment">// Create a single block.  blk is NULL; no need to delete it.</span></div><div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;        cap = 1;</div><div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;        blk = <span class="keyword">new</span> Blk[1];</div><div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;        len = 1;</div><div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;        blk[0] = Blk(x);</div><div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;    }</div><div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;}</div><div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;</div><div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;<span class="comment">/* Ditto, but first check that x is nonnegative.  I could have put the check in</span></div><div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;<span class="comment"> * initFromPrimitive and let the compiler optimize it out for unsigned-type</span></div><div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;<span class="comment"> * instantiations, but I wanted to avoid the warning stupidly issued by g++ for</span></div><div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;<span class="comment"> * a condition that is constant in *any* instantiation, even if not in all. */</span></div><div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> X&gt;</div><div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;<span class="keywordtype">void</span> BigUnsigned::initFromSignedPrimitive(X x) {</div><div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;    <span class="keywordflow">if</span> (x &lt; 0)</div><div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;        <span class="keywordflow">throw</span> <span class="stringliteral">&quot;BigUnsigned constructor: &quot;</span></div><div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;            <span class="stringliteral">&quot;Cannot construct a BigUnsigned from a negative number&quot;</span>;</div><div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;    <span class="keywordflow">else</span></div><div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;        initFromPrimitive(x);</div><div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;}</div><div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;</div><div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;<span class="comment">// CONVERSION TO PRIMITIVE INTEGERS</span></div><div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;</div><div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;<span class="comment">/* Template with the same idea as initFromPrimitive.  This might be slightly</span></div><div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;<span class="comment"> * slower than the previous version with the masks, but it&#39;s much shorter and</span></div><div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;<span class="comment"> * clearer, which is the library&#39;s stated goal. */</span></div><div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> X&gt;</div><div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;X BigUnsigned::convertToPrimitive()<span class="keyword"> const </span>{</div><div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;    <span class="keywordflow">if</span> (len == 0)</div><div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;        <span class="comment">// The number is zero; return zero.</span></div><div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;        <span class="keywordflow">return</span> 0;</div><div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len == 1) {</div><div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;        <span class="comment">// The single block might fit in an X.  Try the conversion.</span></div><div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;        X x = X(blk[0]);</div><div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;        <span class="comment">// Make sure the result accurately represents the block.</span></div><div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;        <span class="keywordflow">if</span> (Blk(x) == blk[0])</div><div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;            <span class="comment">// Successful conversion.</span></div><div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;            <span class="keywordflow">return</span> x;</div><div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;        <span class="comment">// Otherwise fall through.</span></div><div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;    }</div><div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;    <span class="keywordflow">throw</span> <span class="stringliteral">&quot;BigUnsigned::to&lt;Primitive&gt;: &quot;</span></div><div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;        <span class="stringliteral">&quot;Value is too big to fit in the requested type&quot;</span>;</div><div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;}</div><div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;</div><div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;<span class="comment">/* Wrap the above in an x &gt;= 0 test to make sure we got a nonnegative result,</span></div><div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;<span class="comment"> * not a negative one that happened to convert back into the correct nonnegative</span></div><div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;<span class="comment"> * one.  (E.g., catch incorrect conversion of 2^31 to the long -2^31.)  Again,</span></div><div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;<span class="comment"> * separated to avoid a g++ warning. */</span></div><div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> X&gt;</div><div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;X BigUnsigned::convertToSignedPrimitive()<span class="keyword"> const </span>{</div><div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;    X x = convertToPrimitive&lt;X&gt;();</div><div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;    <span class="keywordflow">if</span> (x &gt;= 0)</div><div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;        <span class="keywordflow">return</span> x;</div><div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;    <span class="keywordflow">else</span></div><div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;        <span class="keywordflow">throw</span> <span class="stringliteral">&quot;BigUnsigned::to(Primitive): &quot;</span></div><div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;            <span class="stringliteral">&quot;Value is too big to fit in the requested type&quot;</span>;</div><div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;}</div><div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;</div><div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;<span class="preprocessor">#endif</span></div><div class="ttc" id="class_big_unsigned_html"><div class="ttname"><a href="class_big_unsigned.html">BigUnsigned</a></div><div class="ttdef"><b>Definition:</b> BigUnsigned.hh:13</div></div>
<div class="ttc" id="class_numberlike_array_html"><div class="ttname"><a href="class_numberlike_array.html">NumberlikeArray</a></div><div class="ttdef"><b>Definition:</b> NumberlikeArray.hh:21</div></div>
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